Quantum Technology beyond the Dark Matter

“Nature hides her secret because of her essential loftiness, but not by means of ruse.”

Dark matter is modeled is quantum mechanics and quantum field theory using a second quantized version of electrons, photons, neutrinos, quarters etc. However, a satisfactions picture unifying quantum mechanics with gravity appears naturally only if we use symmetry and super-symmetry theory in which each particle moves not along a world line but rather along a world-sheet, that is, at any time T, we use a stratify of 26 dimensions to model the particle configuration. A study can be looked upon in quantum mechanics as an infinite sequence of harmonic oscillators satisfying Boson commutation relation and the corresponding Fourier components of the study energy-momentum tensor satisfies the Virasoro Lie algebra commutation relation. String theory is the natural component in preference to particle theory because it is well known that conformed in combined with quantum field theory for propagators naturally leads to the Einstein field equations.

In the Higgs mechanism, the process of spontaneous symmetry breaking (SSB) of a local symmetry (i.e. where the transformation is dependent on space-time coordinates) is responsible for quanta of certain fields to acquire a mass. This can be understood by the following discussion. In gauge field theories, the Lagrangian is expected to obey certain symmetries owing to physical requirements. A gauge is a mathematical construction used to eliminate redundant degrees of freedom in a field. It is required that the physical observables should not change under allowed gauge transformations. The symmetry of the Lagrangian implies a transformation which leaves it invariant. These symmetries could be discrete as well as continuous. Discrete symmetries take the form of charge, parity and time reversals. Continuous symmetries require the notions of differentiability and are considered as Lie groups. Associated with a Lie group is the algebra of its infinitesimal generators, which is called Lie algebra. The Higgs field is scalar. Below a critical temperature, due to local SSB, this field interacts with particles to give them their mass. The quantum of the Higgs field is called the Higgs boson. This, or at least a very similar particle, was recently detected at Large Hadron Collider, CERN. Most importantly, the Higgs mechanism explains the mass of the gauge bosons and electroweak theory. This is the non-Abelian gauge theory of weak and electromagnetic interactions, which is a gauge theory with the symmetry group. The weak interaction is mediated by the 3 afore-mentioned bosons and the electromagnetic interaction by its massless quantum, the pho-ton. Work is going on at pace in this field, in Large Hadron Collider (LHC) in Switzer-land, and the experiments determined the mass of the Higgs boson to be both 126.6 GeV and 123.5 GeV which is in the range of perturbation theory. But now CERN researchers are planning to increase the size, which will fall in the non perturbative range, which will affect the quantum mechanics of the system.

After 1925, the major players in quantum mechanics were Heisenberg, Schrödin-ger, Dirac and Max Born. Heisenberg proposed a new type of mechanics called matrix mechanics to explain the spectral lines of atoms. He suggested that observables like position, momentum, angular momentum and energy should be represented not by real numbers but by matrices with the row and column indices corresponding respectively to the initial and final states of the atom during the radiation process. Heisenberg also gave an intuitive explanation of the uncertainty principle stating that both the position and momentum of a particle cannot be measured simultaneously with infinite accuracy. This principle was proved much later rigorously by Hermann We using Dirac’s operator theoretic formalism of quantum mechanics. According to classical physics, the position and velocity of a particle can be calculated simultaneously to arbitrary precision. But in quantum mechanics, the accuracy with which we can measure the momentum and position simultaneously is dictated by Heisenberg’s uncertainty principle. Further, De-Broglie’s hypothesis states that every moving particle has a wave function associated with it. This wave function, however, spreads throughout the space and cannot be localized. Everything came together in 1926 when E.Schrödinger proposed his famous wave equation. Heisenberg developed the theory of quantum mechanics using infinite matrices to represent observables, and he was the first person who applied it to the Hydrogen atom. The same year, Dirac, Born, Heisenberg and Jordan have obtained a complete formulation of quantum mechanics that could be applied to any quantum system. Schrödinger gave the wave mechanics approach to quantum theory using which he was able to arrive at the energy spectrum of the Hydrogen atom by solving an Eigen value problem while Heisenberg gave a matrix mechanics approach to the quantum mechanics which although being conceptually clear, was not suitable for practical calculations. It was finally Dirac who unified both the Schrödinger and Heisenberg pictures by showing that both pictures lead to the same value of the average of an observable in a state. Dirac also presented a new method to arrive at the Lie bracket or commentator of Heisenberg mechanics just by exploiting the properties of the Poisson bracket of classical mechanics. Finally, Dirac derived a relativistic wave equation of the electron by factoring the relativistic Einstein energy-momentum relation with linear factors using 4 × 4 anti-commuting matrices. Dirac’s wave equation is at the heart of modern quantum field theory as developed later by Feynman, Schwinger and Tomonaga. Moreover, super-symmetry theory obtained by using both Bosonic and fermionic strings with an action invariant under super symmetry that trans-forms Bosonic strings to fermionic strings phenomena in quantum gravity. A consistent theory of dark matter and gravitational field produced by it can be developed by modeling dark matter as an aggregate of bosonic and fermionic strings and the action for the gravitational part using the Einstien Hilbert action. Moreover, string theory naturally sets in the dimension of space-time, unlike particle quantum technology.

“A cosmic mystery of immense proportions, once seemingly on the verge of solution, has deepened and left astronomers and astrophysicists more baffled than ever. The crux is that the vast majority of the mass of the universe seems to be missing.”